Binding of metal ions by phytosiderophores. The pKa values for different functional groups in PDMA (Figure 1) are: pKa1 = 2.01, pKa2 = 2.47, pKa3 = 3.12, pKa4 = 7.63, and pKa5 = 9.23 (Suzuki et al., 2021). It is worth noting that PDMA has very basic pKa6 (i.e., pKa > 14) associated with the terminal α-hydroxyl group. For DMA, the dissociation constant for the α-hydroxyl group has been estimated to be 10‑17.1 by using the Taft equation (Perrin 1981); based on the similarity of the molecules, we assume the pKa6 to be the same for PDMA.
Siderophore complexes with metal ions have been shown to change with the pH-dependent protonation state of the siderophore (Kim, Duckworth, and Strathmann 2009). We modelled metal-PDMA to undergo deprotonation reactions as the pH increased during the titration from an initially acidic solution (pH = 2.6):

where successive deprotonation reactions free up electron pairs and create a more negative charge in PDMA to produce stronger PDMA metal interactions.
The terminal α-hydroxyl group is not thought to bind with divalent metal ions at pH values in the range of our titrations, resulting in a pentadentate complex at the high pH end (Murakami et al. 1989). However, it is worth noting that strongly Lewis acidic trivalent cations are thought to form hexadendate complexes (e.g., Fe(III)DMA3-) where the final α-hydroxyl group deprotonates and bonds to the ligand (Murakami et al. 1989). This has led to some inconsistences in the reporting of stability constants. For example, the Fe(III)DMA complex stability constant has been reported as 15.7-31.35, dependent on whether MIIHDMA3- (logβ111) or MIIDMA4- (logβ110) was used as the reference state, where logβMLH represents metal ion, ligand, and protons present, respectively. (Shenker, Fan et al. 2001, Dell'mour, Koellensperger et al. 2010) It is worth noting that, when the stability constant is corrected for the deprotonation of the α-hydroxyl group, the logβ110 shows a difference between Fe(III) and divalent cations that more is typical of other siderophores and ligands with hard base binding moieties (Supplementary Information Table S1).
Spectrophotometric titrations of metal-PDMA solutions. The UV-visible spectra of metal-PDMA complexes during titrations are shown in Figure 2. For PDMA complexes with Co(II), Zn(II), Cu(II), and Ni(II), spectral shifts were observed as the solution changed from low to high pH, reflecting changes in light absorption among the intermediate species in equation 1. For example, solutions with Co(II) and PDMA, a shift of Amax was observed from 262 to 272 nm, with a 0.2 unit absorbance increase (Figure 1). In contrast, Mn(II) does not show a spectral shift in the UV-visible range.
Determination of Stability Constants. Using the spectrophotometric titration data, we calculated the stability constants for MIIHPDMA3- (Logβ111), with Mn(II), Ni(II), Cu(II), Co(II), and Zn(II), in KEV (Table 1). The resulting stability constants are similar to those previously obtained stability constants for other phytosiderophores, such as mugineic acid (MA), 2’- deoxymugineic acid (DMA), 3-hydroxymugineic acid (HMA) and 3-epi-hydroxymugineic acid (epi-HMA) (supplementary material Table S1). The Fe(III)PDMA3- stability constant was previously determined by Suzuki et al. (2021), and adjusted to logβ011 = 34.2, considering the deprotonation of the α-hydroxyl group.
Lewis acidity and binding. The affinity of ligands for metal ions has previously been correlated to several parameters, including ionic potential, and hydrolysis constant (KOH) of cations (Hernlem, Vane, and Sayles 1999; Hancock and Martell 1989). These correlations not only provide insights into the interactions between binding ligands and metal ions, they can facilitate the estimation of affinity constants for metals for which there is no experimental data (Duckworth, Akafia et al. 2014).
Because ligand complexation is fundamentally a Lewis acid-base interaction, some aspects of siderophore stability constants can be attributed to the hard-soft acid/base theory. Figure 3a presents a linear correlation of logβPDMA with the ionic potential (z/r) of the corresponding metal ion (R2 = 0.87). This phenomenon can be rationalized by noting that the Pearson's hardness of the metal ion is related to the strength of interaction with the Lewis bases in the siderophore binding moieties. Similarly, Figure 3b presents a correlation of logβPDMA versus the logarithm of the hydrolysis constant (logβOH) (R2 = 0.96). Because siderophores feature negatively charged oxygen donor groups (in the case of PDMA, carboxylate groups and a hydroxyl group), it is assumed that the ability of the metal ion to attract the binding groups on the ligand trends with the affinity of the metal ion for hydroxide ions (Hernlem, Vane, and Sayles 1999).
Despite its utility in explaining fundamental chemistry, Hernlem et al. (1999) noted that using z/r as a predictor of unknown ligand-metal stability constants may be superfluous because the relationship with logβOH yields a stronger correlation (Figure 3). The resulting equation, which may be used to estimate stability constants from tabulated hydrolysis constants, is:

where logβ is the β110 or the β111 depending on the metal in question. Estimates of PDMA stability constants determined by equation 2 are presented in the supporting information (supplementary material Table S2).
Estimation of phytosiderophore stability. Unlike structurally diverse microbial siderophores, phytosiderophores are closely structurally related{Hider, 2010 #39}. As seen in the Figure 1, the main difference between phytosiderophores is the presence and position of hydroxyl groups not associated in metal binding. Synthetic PDMA has the added change of having a five membered ring instead of a four membered ring, making it more resistant to microbial degradation in the rhizosphere environment than natural phytosiderophores (Suzuki et al. 2021). The homology of these ligands suggest commonalities in the binding affinities of these ligands.
To that end, we constructed log-log plots of the stability constants for PDMA that we determined against known literature stability constants for the other phytosiderophores, as well as the commonly used trishydroxamate siderophore DFOB. Regressions for all the siderophores with PDMA show strong linear trends, with R2 = 0.90–0.94 (Table 2). Because PDMA is easier to obtain, more stable and more inexpensive than a lot of other phytosiderophores such as mugineic acid (MA), 2’-deoxymugineic acid (DMA), 3-hydroxymugineic acid (HMA) and 3-epi-hydroxymugineic acid (epi-HMA), it could be used as an alternative to these siderophores, and as a predictor of metal stability constants with MA, DMA, HMA and epi-HMA.
When regressing the stability constants for PDMA with those of the trishydroxamate DFOB, an R2 = 0.97 was observed from the relationship:

This correlation was previously discounted because of the aforementioned inconsistencies in reporting of the hexadentate Fe(III) binding constants (with phytosiderophore constants being orders of magnitude smaller than DFOB) and the structural differences between the ligands (viz. amine groups associated with complexation by PDMA). Because DFOB has a large thermodynamic database of siderophore-metal ion interactions, using DFOB as a predictor for PMDA, and potentially other phytosiderophores, could allow for estimation of a large number of ions that may be used in models of siderophores in the environment.
Table S2 shows estimated binding affinities for PDMA as calculated by equations 2 and 3 (e.g., estimation from hydrolysis and DFOB binding constants). In general, estimated errors are lesser for logβ estimated constants than from hydrolysis constants. In general, there is reasonable agreement (difference been Logβ values less than 2) for divalent cations as well as Al(III) and Ga(III). Greater discrepancies appear for large cations that have non-octahedral or pentadentate coordination (e.g., La(III) or Pb(II) and hard cations with high affinities (e.g., In(III), Co(III), and Mn(III)). Previous studies have noted that for hard ions, steric effects may have significant impacts on the relative affinity for specific metal ions (Harrington et al. 2012). This suggest that caution may be needed when estimating the binding constants of ligands that have differing coordination chemistries (e.g., steric contracts, moiety preorganization, or complex architectures). The values in Table S2 provide potential end member estimates for phytosiderophores with metal ions that lack values, as well as illustrate the limits of this approach, and may help to guide future measurements to improve our ability to estimate logβ values.